Incorporation and Characterization of a Mixing Elbow on the Pilot

However, for the purposes of the present work, we have assumed that mixing down to the Kolmogorov scale is rapid and that momentum diffusion is the ...
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GENERAL RESEARCH Incorporation and Characterization of a Mixing Elbow on the Pilot Plant Scale for a Mixing Sensitive Crystallization of an API Utpal K. Singh,* Glenn Spencer, Rich Osifchin, Jose Tabora, Omar A. Davidson, and Charles J. Orella Chemical Engineering R&D, Merck & Co., Inc., Rahway, New Jersey 07065

A mixing elbow was, for the first time, characterized on the pilot plant scale using the Fourth Bourne Reaction to obtain a correlation for mixing time using the approach of Johnson and Prud’homme and Mahajan and Kirwan. The elbow was applied for a semicontinuous mixing sensitive crystallization of an API (Active Pharmaceutical Ingredient) on the pilot plant scale to offer a means of controlling secondary nucleation and providing rapid mixing to eliminate local regions of high supersaturation. The application of the mixing elbow for the API crystallization resulted in a change in particle morphology in the form of single crystals rather than dense agglomerates that were observed in the absence of a mixing elbow. Introduction Scale sensitivity of crystallization is, at least in part, due to secondary nucleation effects that are dependent on, among other factors, vessel/agitator geometry and mixing times, which make scale-up of crystallization processes with particle size control difficult in conventional equipment.1-4 Additionally, scale-up difficulties are also encountered when process time scales, i.e., crystallization and/or reaction time scales, are faster than mixing times in stirred tank reactors. Such processes have been addressed in the past using impinging jet mixers1,2 and mixing elbows5 which provided rapid micromixing in a controlled geometry that is invariant with scale. These and other static mixers have been characterized using the Bourne Reactions to develop empirical correlations for mixing time.1,2,6,9,10 The present report applies earlier laboratory scale studies of Kirwan and Mahajan2 and Johnson and Prud’homme for confined impinging jets and vortex mixers2,6 to develop an empirical correlation for mixing time in mixing elbows on the pilot plant scale. To the best of our knowledge, this is the first time that pilot plant scale mixing elbows have been quantitatively characterized; and the results are applied to a mixing sensitive crystallization of an API on the pilot plant scale to show the effect of mixing on particle size distribution and morphology. Experimental Mixing Elbow Characterization on the PP Scale s Fourth Bourne Reaction. Mixing studies using the Fourth Bourne Reaction were conducted in three 200 gallons vessels as shown in Figure 1 below. The procedure involves a “once-through” mixing of a stream containing an aqueous solution of 2,2-dimethoxypropane (DMP), ethanol, and NaOH with a dilute aqueous HCl * To whom correspondence should be addressed. E-mail: [email protected].

solution at 20 °C with a 1:1 molar ratio of HCl and DMP and an excess of NaOH. The mixing of the two streams results in the following two reactions k1

NaOH + HCl 98 H2O + NaCl

(1)

k2

H2O + C5H12O2 + HCl 98 2CH4O + C3H6O + HCl (2) where the rate constant for the acid base neutralization and the DMP (2,2-dimethoxypropane) hydrolysis are 1.4 × 108 m3/mol/s and 0.6 m3/mol/s, respectively.1 Consistent with definitions in the literature, the reaction time scale is then defined as τrxn: 1/(k2*Co) where k2 is the rate constant of the slow reaction (reaction 2) and Co is the DMP concentration after mixing of the two streams assuming no reaction were to occur. The mixing effectiveness is measured by the extent to which the slow reaction (eq 2) occurs and is quantified as follows

Xs )

[MeOH]outlet 2[DMP]inlet

(1 + F1)

(3)

where F, [MeOH]outlet, and [DMP]inlet are the flow ratio of the HCl and DMP streams (QDMP/QHCl), methanol concentration at the outlet of the mixing elbow, and initial DMP concentration in TA-2, respectively. It should be noted that stability of the reactant and product streams have been confirmed before under the conditions studied,1 and no composition change was observed after sampling. A HCl solution with the desired concentration was made in TA-1, while the DMP (2,2-dimethoxypropane), punctillious ethanol, NaOH, and DI water solution was made in TA-2. The DMP solution makeup required addition of water, ethanol, and NaOH prior to charging DMP to suppress the undesired hydrolysis. The DMP concentration was fixed by the desired reaction time

10.1021/ie048987r CCC: $30.25 © 2005 American Chemical Society Published on Web 04/21/2005

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Figure 1. Pilot plant setup for conducting mixing studies using the Fourth Bourne Reaction.

scale for each run, and subsequent concentrations were determined by the requirement that the molar ratio of DMP:HCl be 1:1. Both solutions were maintained at 20 °C and were recycled around the respective vessels using a centrifugal pump. A bleed from the two recycle lines were directed to the mixing elbow via massmeter controlling the flowrate with a needle valve to ensure that the molar constraint is satisfied. The mixed stream was sampled 35 diameters downstream of the mixing point prior to flowing into a waste collection tank. The inner diameters of the mixing elbow were 5 mm and 22 mm (D/d ) 4.4), and the DMP and NaOH were charged to the elbow via the larger diameter pipe and HCl via the smaller of the two pipe diameters. The composition at the outlet was analyzed via a gas chromatograph equipped with a 30 m RTX-1701 column (0.32 mm i.d. column at 50 °C with injection temperature at 50 °C). Each set of experiments was conducted by proportionately increasing the flow rate of the HCl and DMP streams maintaining the required molar ratios, with fixed reaction time scale, flow ratio, and velocity ratio while varying only the Reynolds numbers of the two streams. Reaction time scales from 10 to 108 ms were investigated with the Reynolds number for the DMP, HCl, and exit stream ranging from 1000 to 13000, 76033000, and 1200-16000 for the DMP, HCl, and exit streams, respectively. Semicontinuous Crystallization of an API with a Mixing Elbow. Semicontinuous crystallization of an API was conducted by first generating the seed bed (15% seed loading) by wet-milling API (Active Pharmaceutical Ingredient) in 1:1 toluene:heptane at 20 °C using a rotor stator wet mill with 3 superfine generators yielding 14 micron particles. API (150 g/L) in toluene at 50 °C and N-heptane at 20 °C were then added simultaneously over 3 h, while continuously maintaining the 1:1 heptane:toluene ratio over the entire charge. The effect of mixing on the final particle size distribution and morphology was probed by examining four different addition modes for the crystallization including the following: (a) direct addition to crystallizer with slow agitation, i.e., just sufficient to suspend the particles (30 rpm - 1.3 m/s); (b) direct addition to crystallizer with

rapid agitation (120 rpm - 4.3 m/s tip speed); (c) half elbow; and (d) full elbow. A schematic of the half elbow and the full elbow is shown in Figure 2 below. In both cases the slurry in the crystallizer is continuously recycled via the elbow. The half elbow (Figure 2a) requires addition of API in the toluene solution at 50 °C to the elbow for rapid mixing with the recycling seedbed, while the antisolvent, N-heptane, is added directly to the vessel via a 3/8” subsurface line. The full elbow (Figure 2b), on the other hand, requires addition of both the hot API in toluene solution and N-heptane directly to the elbow. In both cases the charge rates were adjusted to maintain a 1:1 toluene:heptane solution in the crystallizer. In addition, the flowrate of the recycle stream was set to be ten times the flowrate of the individual N-heptane or API in toluene solution. The setup for pilot plant runs of the semicontinuous crystallization with a full mixing elbow is shown in Figure 3 below. The crystallizations required three 200 gallon vessels containing 150 g/L API in toluene at 50 °C, heptane at 20 °C, and 1:1 toluene:heptane solution containing the 15% wet-milled seed. The crystallizations with the full elbow were initiated by recycling the seed bed in TA-3 via the mixing elbow prior to starting the flow of the hot batch and the antisolvent stream into the elbow. The total time for stabilizing all the flow rates was approximately 5-10 min (compared to an overall charge time of 3 h), and all flow rates were monitored throughout the course of the crystallization using a 1/2” Hastelloy C Micromotion Mass flow meters. The 200 gallon crystallizer was equipped with a CBT (curved blade turbine) agitator with a maximum agitation speed of 120 rpm (4.3 m/s tip speed). Particle size distribution were measured on the final dry cake using Honeywell Microtrac ASVR. Results and Discussion Characterization of a Mixing Elbow. Mixing elbows of the type studied in the present report have been examined before in the literature using flow visualization studies and the second Bourne Reaction10,11 on the lab-scale; however, no pilot plant scale data are available in the open literature. Tosuns’s

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Figure 2. Schematic of (a) half elbow and (b) full elbow.

Figure 3. Process flow diagram for semicontinuous crystallization of API in the presence of a mixing elbow.

results indicate an optimum velocity ratio at a given diameter along with increased mixing effectiveness with

increasing the Reynolds number up to a value of 1000 after which the mixing effectiveness was invariant with

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present work, we have assumed that mixing down to the Kolmogorov scale is rapid and that momentum diffusion is the rate-limiting step. Based on the momentum diffusion mechanism and assuming that the energy dissipation is characterized by the kinetic energy of the high energy stream, i.e., HCl stream, the following relationship has been derived for mixing two streams with similar densities and a flow ratio of unity1,2,6

υ0.5 HCl τmix,F)1 ) K 1.5 uHCl

Figure 4. Scaling of the conversion of the slow reaction (reaction 2) to the linear velocity of the HCl stream for a flow ratio of 1.4, 1.2, and 1.6 for a reaction time scale of 10, 16, and 86 ms, respectively.

increasing the Reynolds number. No mixing time correlation was reported since information about the mixing volume, i.e., the volume over which kinetic energy is dissipated, was not available. The procedure developed by Johnson and Prud’homme1,6 circumvents this problem by assigning a conversion for the fourth Bourne Reaction at which, they claim, mixing time equals the reaction time. Application of this approach allows the mixing volume to be lumped in with a proportionality constant that can subsequently be determined at a conversion of 0.04, where the Damkohler number, defined as the ratio of mixing time to reaction time, has a value of unity. Alternatively, we could have taken the midpoint of the conversion range as the point where mixing and reaction times are identical; however, for the sake of consistency, we have adapted the formulation developed by Johnson and Prud’homme. As the first step in determining the mixing time correlation, it was necessary to determine the governing mixing mechanism, i.e., turbulent diffusion, momentum diffusion, or mass diffusion. Mechanism discrimination can be conducted by determing the scaling of mixing time with respect to linear velocity and kinematic visocity, and the work of Johnson and Prud’homme has shown that this is tantamount to determining the scaling of the conversion of the slow reaction to linear velocity and kinematic viscosity. The scaling of the selectivity to the slow reaction with linear velocity of the HCl stream is shown in Figure 4. Bulk blending, i.e., macromixing, is governed primarily by the inertial convective or turbulent diffusion process which exhibits an inverse dependency on linear velocity; while a 1.5 order dependency is exhibited by mass diffusion and momentum diffusion mechanisms. Mass diffusion cannot be completely discounted since the scaling with respect to the kinematic visocosity was not measured; however, for Schmidt numbers used in the present study, i.e., 1500, momentum diffusion has been shown to be slower than mass diffusion.12 As a result, all results in this paper are assumed not to be governed by mass diffusion. The slope along with the 95% confidence intervals for the three runs shown in Figure 4 are -0.3 ( 0.9, -0.9 ( 1.0, and -1.25 ( 0.4 for the 10, 16, and 86 ms runs, respectively. The uncertainty in the data evidenced by the 95% confidence intervals does not allow us to distinguish between the momentum and turbulent diffusion mechanisms. However, for the purposes of the

(4)

where k, n, and u are proportionality factor (including the mixing volume), kinematic viscosity of the HCl stream, and linear velocity of the HCl stream, respectively. A similar equation was obtained by Kirwan and Mahajan using a different approach.2 The proportionality factor K was determined by equating the Damkohler number, defined as the ratio of mixing time to reaction time, to a value of unity for experimental conditions obtained at a flow ratio of unity yielding 4% conversion to the slow reaction. As mentioned before, this value was selected based on the formulation set forth by Johnson and Prud’homme.1 The resulting value of K for a mixing elbow was 750 m0.5. It should be stressed that the resulting expression for mixing time holds for a mixing elbow with the geometry studied (d/D ) 4.4). Similar constants have been reported by Johnson and Prud’homme for impinging jets and vortex mixers; however, a direct comparison is difficult due to geometry differences and the fact that the effect of diameter and the diameter ratio was not investigated in the present study. In addition, the present study was conducted in the Pilot plant scale with the average Reynolds number ranging from 760 to 33 000 compared to a range of 1003000 for impinging jets and vortex mixers. Nevertheless, a qualitative comparison of the mixing times can be instructive. Table 1 shows a comparison of mixing times in various static mixers under similar flow conditions with linear velocity of 1 m/s, but varying diameters. The overall mixing times obtained with mixing elbows are faster than vortex mixers and of the same magnitude as the impinging jets. Characteristic mesomixing times by turbulent diffusion can be calculated as follows7,8

τmeso )

( )

πd2 uHCl 4Dt uDMP

(5)

where d, Dt, uHCl, and uDMP are, for the case of the mixing elbow, the diameter of the small arm of the mixing elbow (5.0 mm), turbulent diffusivity, linear velocity of the HCl stream (1 m/s), and linear velocity of the DMP stream at a flow ratio of unity and diameter ratio of 4.4. The turbulent diffusivity is calculated to be 1.43 × 10-3 m2/s at 1 m/s with an energy dissipation of 157 W/kg.7,8 The resulting mesomixing time is then calculated to be 271 ms compared to a value of 2 ms for micromixing from the engulfement model.1,8 The mesomixing time is approximately the same order of magnitude as the mixing time calculated in Table 1, whereas the calculated micromixing time is significantly lower than that calculated in Table 1. Micromixing was assumed to be the rate determining step in the analysis above; however, the scatter in the data in Figure 4 along with the variation in observed micromixing times with

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Table 1. Qualitative Comparision of Mixing Times in Various Static Mixers at a Flow Ratio of One and a Linear Velocity of 1 m/s Reynolds number

diameter

mixing time correlation 0.5 υoutlet

impinging jets

100-3000

d ) 2.53 mm, D/d ) 4.76

τmix,F)1 ) 1470

vortex mixers

50-2500

d ) 2.53 mm, D/d ) 4.7

τmix,F)1 ) 16 000

mixing elbow

1100-33 000

d ) 5.0 mm, D/d ) 4.4

τmix,F)1 ) 750

that calculated suggests that it is not possible to distinguish between the two operating mechanisms in the present report. In fact, both mechanisms may be operating as the rate determining step at different conditions. By analogy to vortex mixers, flow ratios greater than 1 are expected to have a detrimental effect on mixing efficiency. In other words, larger flow ratios require higher linear velocities to obtain similar conversion.6 The quantitative effect of flow ratios greater than unity on mixing time has been empirically determined for vortex mixers. The empirical correlation was defined, for a given reaction time, as the ratio of the velocity to obtain a conversion of 0.04 at a given flow ratio to the velocity to obtain a conversion of 0.04 at a flow ratio of unity. This ratio was empirically found to be (1.2*Ln(F) + 1) for vortex mixers,6 and for the purposes of the present study, a similar correlation was assumed to hold for mixing elbows: i.e., velocity ratio ) R*Ln(F) + 1 where R is an adjustable parameter varied to obtain the best correlation of mixing efficiency with the Damkohler number, τmix/τrxn. The resulting mixing time expression then becomes

[ ( ) ]

QDMP υ0.5 τmix ) K 1.5 RLn +1 QHCl u

-1.5

(6)

Figure 5 shows a plot of the conversion to the slow reaction as a function of the Damkohler number, calculated using the above expression for mixing time with R ) 0, for the Reynolds number, and the flow ratio ranging from 10 to 108 ms, 760-33 000, and 0.8-7.3, respectively. Values of R greater than zero resulted in

Figure 5. Correlation of the Damkohler number (tmix/trxn) to mixing efficiency in a mixing elbow for R ) 0. Trxn in the legend describes the reaction time scale defined in text.

mixing time (s)

ref

0.4

1

1.5 0.5

(D/d) d

u1.5 DMP2x2 0.5 υoutlet

23

u1.5 DMP

0.5 υoutlet

6

1

u1.5 DMP

significantly greater scatter in the data indicating the absence of a significant effect of the flow ratio on the mixing time under the conditions studied in the present paper. This result is surprising especially in light of the results of the vortex mixer mentioned above; however, the effect of the flow ratio for mixing elbows may be subtle and cannot be distinguished from the experimental uncertainty. It should be noted that the linear velocity used in Figure 4 as well as eqs 4 and 6 and the correlation in Figure 5 is that for the HCl stream which has the highest linear velocity and hence the highest kinetic energy. Utilizing the linear velocity of the outlet stream or DMP stream resulted in increased scatter in the graph in Figure 5. The correlation of data under widely varying conditions with the Damkohler number indicates that the mixing time expression in equation 4 is, at least phenomenologically, descriptive of the mixing elbow. Table 2 displays the flow conditions and concentrations for the data presented in Figure 5. Table 2. Raw Data Showing the Flow Conditions and the Concentrations for the Data Displayed in Figure 5 flowrates

concentration

DMP (kg/min)

HCl (kg/min)

DMP (M)

NaOH (M)

HCl (M)

conversion to slow reaction

2.3 6.8 11.4 15.9 20.4 25.0 28.4 11.3 15.9 20.4 25.0 15.9 11.4 6.8 2.3 11.4 2.3 20.4 18.2 13.6 20.2 18.0 13.5 11.2 9.0 6.7 4.5 2.3 20.2 13.5 6.8 4.5 2.3 13.5 6.8

0.33 0.97 1.57 2.27 2.87 3.49 3.98 3.51 4.96 6.36 7.75 13.00 9.30 5.50 1.85 13.41 2.68 14.22 12.64 9.48 12.56 11.17 8.37 6.98 5.58 4.19 2.79 1.40 12.56 13.95 6.99 4.65 2.33 13.95 6.98

0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.19 0.18 0.18 0.18 0.18 0.27 0.27 0.27 0.27 0.27 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03 0.03

0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.37 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.36 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05

1.42 1.42 1.42 1.42 1.42 1.42 1.42 0.63 0.63 0.63 0.63 0.24 0.24 0.24 0.24 0.24 0.24 0.40 0.40 0.40 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.05 0.03 0.03 0.03 0.03 0.03 0.03

0.50 0.40 0.32 0.39 0.34 0.30 0.38 0.24 0.16 0.27 0.22 0.05 0.04 0.06 0.24 0.06 0.17 0.06 0.03 0.06 0.02 0.02 0.03 0.06 0.03 0.11 0.13 0.20 0.01 0.02 0.02 0.04 0.04 0.03 0.02

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Figure 6. Effect of the mixing intensity on the particle size distribution during semicontinuous API crystallization.

The mixing effectiveness of static mixers with various geometries has been studied9-11 in the open literature, and in particular Tosun has characterized similar mixing elbows using the Second Bourne Reaction.10 Their data can also be reformulated in the context of the present work to show that the selectivity to the slow reaction could correlate with the Damkohler number; however, their data could not be used to confirm the mixing time correlation above since the benchmark value of conversion for the second Bourne Reaction at which the reaction time equals the mixing time is unknown. Crystallization with a Mixing Elbow on the Pilot Plant Scale. The mixing elbow was applied to study an API crystallization that has been shown to be scale and geometry sensitive due to strong secondary nucleation effects, and the crystallization time scale was of the order of milliseconds. Hence, there was a significant driver to develop a process that would be more amenable to scale-up by controlling secondary nucleation effects and providing a means for rapid mixing to eliminate local regions of high supersaturation. We had hoped to accomplish this by using a mixing elbow, which would circumvent blending issues, exhibit shorter mixing time scales, and allow more controlled secondary nucleation that may be independent of agitator geometry. It should be noted that use of a mixing elbow still requires an agitator in the crystallizer vessel for particle suspension

and as a result we cannot completely rule out sensitivity to agitator geometry. However, it should be noted that no particle breakage or secondary nucleation effects were observed in the absence of supersaturation in the crystallizer. Additionally, crystallization time scale is of the order milliseconds which is orders of magnitude faster than residence time in the mixer; therefore, all secondary nucleation effects occurred in the mixing elbow and not in the agitated vessel suggesting that the observed secondary nucleation effects may be independent of agitator geometry. Figure 6 shows the effect of mixing intensity on the particle size distribution. Increasing mixing intensity decreased the average particle size from 132 microns for crystallizations performed with agitation just sufficient to suspend the particles (1.3 m/s tip speed) to 102 microns with a faster agitation (4.3 m/s tip speed). Further increase in mixing intensity using a half and full elbow decreased the particle size to 63 and 41 microns, respectively. With the exception of the experiment with low agitation, all experiments yielded a narrow unimodal particle size distribution. The particle size distribution from the low agitation run was bimodal with a tail on the low end of the distribution presumably due to greater secondary nucleation effects for larger particles. The change in particle size distribution with increasing mixing intensity was also accompanied by a change in the particle morphology as shown in Figure 7 below. SEM images of API particles after crystallization using above surface addition of hot batch and subsurface addition of heptane yielded an average particle size around 100 microns consisting of dense agglomerates. Crystallization with half elbow and full elbow also yielded agglomerated particles; however, the degree of agglomeration with the full elbow was lower than that for the half elbow which in turn was lower than that for direct addition to a stirred tank. Additionally, distinct single crystals are evident in the SEM images of the particles from the full elbow. The overall mixing time is a combination of macromixing, mesomixing, and micromixing, and for the case of stirred tanks the rate determining step is usually macromixing. Generalized correlations suggest that macromixing/blending times are inversely proportional to the agitation speed and the time scale on pilot plant scale vessels is of the order of seconds.15,16 Macromixing effects are not significant with mixing elbows since the

Figure 7. Effect of the mixing intensity on the particle morphology during the semicontinuous crystallization of API: (a) full elbow; (b) half elbow; and (c) stirred tank.

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small volumes only require mesomixing for complete blending. Based on the correlation developed earlier, a 72 ms mixing times was calculated under crystallization conditions (linear velocity: 6 m/s, 10:1 mass flowrate ratio), which is of the same order of magnitude as the API crystallization time scale that was determined to be of the order of milliseconds.15 By these arguments, mixing times for the four modes investigated can be ordered as follows:

stirred tank - low agitation > stirred tank high agitation > half elbow > full elbow The use of a mixing elbow in the API crystallization altered both the particle size distribution and particle morphology; however, it is unclear whether the changes are due to rapid mixing times resulting in formation of distinct single crystals and/or a result of high shear conditions resulting in particle deagglomeration. The effect of hydrodynamics on crystals growth properties have been documented in the literature;17 however, it was not possible in the present study to determine whether a similar phenomena was occurring. In addition, the quantitative deconvolution of shear and mixing effects has been discussed in the literature;16 however, the effects of shear were not quantified in the present study. The scale-up of a mixing sensitive crystallization and/ or reaction with a mixing elbow offers a number of advantages to that of scale-up in stirred tank reactors. First, mixing elbows exhibit faster mixing times which can presumably be scaled using the Damkohler number (ratio of mixing time to reaction/crystallization time scales) as the scale-up parameter. In addition, the mixing elbows offer a means to control geometry sensitive effects thereby reducing/avoiding agitator and vessel sensitivity issues that plague the scale-up of mixing sensitive processes. Acknowledgment Hsien-Hsin Tung is gratefully acknowledged for shedding insight into a number of observations reported in the present study and for suggesting the use of a mixing elbow to address the scale-up issues. Brian K. Johnson is also acknowledged for supplying copies of his thesis and paper which serves as the foundation for much of this work as well suggesting the use of the Fourth

Bourne reaction for mixing studies. Lou Crocker is also acknowledged for measuring particle size distributions and obtaining SEM images. Literature Cited (1) Johnson, B. K.; Prud’homme, R. K., Chemical Processing and Micromixing in Confined Impinging Jets. AIChE. J. 2003, 49, 2264. (2) Mahajan, A. J.; Kirwan, D. J. Micromixing effects in a TwoImpinging-jets precipitator. AIChE J. 1996, 42, 1801. (3) Nyvlt, J. Kinetics of Secondary Nucleation with Attrition and the Mean Size of Product crystals From the Continuous Stirred Crystallizer. Collect. Czech. Chem. Commun. 1981, 46, 79. (4) Singh, U. K.; Tabora, J.; Osifchin, R.; Epstein, A. Semicontinuous Mixing Sensitive Crystallization of an API. Manuscript in preparation 2004. (5) Merck & Co., Inc. Internal publication. (6) Johnson, B. K. Flash Nanoprecipitation of Organic Actives Via Confined Micromixing and Block Copolymer Stabilization, Ph.D. Thesis, Princeton University, 2003. (7) Baldyga, J.; Bourne, J. R. Turbulent Mixing and Chemical Reactions; Wiley: England, 1999. (8) Torbacke, M.; Rasmuson, A. C. Influence of Different Scales of Mixing in Reaction Crystallization. Chem. Eng. Sci. 2001, 56, 2459. (9) Bourne, J. R.; Lenzner, J.; Petrozzi, S. Micromixing in Static Mixers: An Experimental Study. Ind. Eng. Chem. Res. 1992, 21, 1216. (10) Tosun, G. A Study of Micromxing in Tee Mixers. Ind. Eng. Chem. Res. 1987, 26, 1184. (11) Cozewith, C.; Busko, M. Design Correlation for Mixing Tees. Ind. Eng. Chem. Res. 1989, 28, 1521. (12) Baldyga, J.; Bourne, J. R. Simplification of Micromixing Calculations: I. Derivation and Application of New Model. Chem. Eng. J. 1989, 42, 83. (13) Fasano, J. B.; Penney, W. R. Cut Reaction Byproduct by Proper Feed Blending. Chem. Eng. Prog. 1991, 46. (14) Fasano, J. B.; Penney, W. R. Avoid Blending Mix-ups. Chem. Eng. Prog. 1991, 56. (15) Togkalidou, T.; Tung, H. H.; Sun, Y.; Andrews, A. T.; Braatz, R. D.; Model-Based Experimental Design and Optimization for Cooling Crystallization of a Pharmaceutical Compound Using In Situ Measurements of Concentration and PSD. Proceedings of 15th International Symposium on Industrial Crystallization, 2002, 497. (16) Ilievski, D.; Rudman, M.; Metcalfe, G. The Separate Roles of Shear Rate and Mixing on Gibbsite Precipitation. Chem. Eng. Sci. 2000, 56, 2251. (17) Chew, C. M.; Ristic, R. I.; Dennehy, R. D.; Yoreo, J. J. Crystallization of Paracetamol under Oscillatory Flow Conditions. Cryst. Growth Des. 2004, 4, 1045.

Received for review October 17, 2004 Revised manuscript received March 5, 2005 Accepted March 14, 2005 IE048987R